Question

A prism of refracting angle 30° is coated with a thin film of transparent material of refractive index 2.2 on the face AC of the prism. A light of wavelength 5500 is incident on face AB such that the angle of incidence is 60°. Find

(a) the angle of emergence, and

(b) the minimum value of thickness of the coated film on the face AC for which the light emerging from the face has maximum intensity. [Given the refractive index of the material of the prism is √3]

Answer 1

(a) From Fig. 12.16, we have

Angle of emergence is zero. (b) The reflected ray 1 is reflected from the denser medium (Fig. 12.17). For the reflected ray 1 there is a phase change of π. There is no change of phase for the second reflected ray 2. Thus the condition of maxima for the reflected rays is

and the condition of maxima for the transmitted rays is